• A novel inverse dynamics formulation derived within a double-step semi-recursive framework for hydraulics. • Analytical computation of valve-level control signals from position references. • Coupling inverse and forward dynamics in unified impedance control. This study presents a novel inverse dynamics formulation derived within a double-step semi-recursive framework for coupled hydraulic-mechanical systems within a model-based control framework. The method enables analytical computation of valve-level control signals from desired position references, making it broadly applicable to real-time control of hydraulic manipulators. The formulation explicitly incorporates nonlinear pressure-flow characteristics of double-acting cylinders, including sign-dependent square-root flow, compressibility, and leakage, thereby extending inverse dynamics consistently down to the valve-control signal level. To demonstrate its effectiveness, the formulation is embedded in an impedance control framework, bridging high-level compliance objectives with low-level hydraulic actuation. Forward dynamics is integrated as a complementary layer to capture nonlinear hydraulic behavior, ensuring physical consistency and real-time feasibility. Numerical simulations on a multi-joint hydraulic crane with double-acting cylinders confirm that the approach suppresses oscillations and maintains precise trajectory tracking under both constant and time-varying loads. Notably, accuracy is preserved even during triangular trajectories with abrupt direction changes, highlighting robustness against dynamic disturbances and complex motions. These results provide methodological insight into hydraulic–mechanical modeling and practical guidance for impedance controller design in heavy-duty hydraulic systems.
Tang et al. (Sat,) studied this question.